Integrated Control Chart System: A New Charting Technique

Transcription

1 Proceedng of the 202 Internatonal Conference on Indutral Engneerng and Operaton Management Itanbul, Turkey, July 3 6, 202 Integrated Control Chart Sytem: A New Chartng Technque M. Shamuzzaman Department of Indutral Engneerng and Management Unverty of Sharah Sharah, UAE Abtract A mult-tage and mult-tream manufacturng ytem ha everal proce tage each of whch cont of one or more tream (e.g. machne) dependng on ome factor (e.g. bottleneck machne, dfferent producton rate). A number of method were developed for mplementng Stattcal Proce Control (SPC) for mult-tream manufacturng procee, but none of them propoed an SPC cheme for a mult-tage and mult-tream manufacturng ytem n an ntegratve and optmal manner. Th artcle revew the bac procedure for the degn of the ntegrated control chart ytem for montorng multtage and mult-tream manufacturng procee. Fnally, ome future reearch drecton are gven. Keyword Qualty control, Integrated control chart ytem, Multtage and mult-tream manufacturng ytem. Introducton Product are typcally fabrcated through varou tage n a manufacturng proce. The ntegraton of all thee tage reult n a multtage manufacturng ytem. In the manufacturng of a mechancal part, each tage correpond to the machnng of a dmenon. The dmenon machned at ome tage are crtcal to the overall qualty of the product and have to be montored by the control chart. A control chart ytem defned a an ntegrated ytem contng of all of the chart ued to montor the crtcal tage of a manufacturng ytem [, 2]. Due to the dfference n producton rate and other factor, ome proce tage may have more than one parallel tream (e.g. machne) (or a ngle machne wth everal head) wth each machne or head performng dentcal operaton or producng dentcal product. In ome applcaton, a ngle Shewhart chart or group chart ued to montor the output from all the tream of a tage. However, a eparate chart can be appled to the output of each ndvdual tream. Th cenaro help to detect and dagnoe the out-of-control tream [3]. Ott and Snee [4] tuded fllng weght data from a machne whch had twenty-four head. The focu of the artcle wa to how a varety of method to analyze the data and the dfferent reult. They ued plot, redual analy and ANOVA technque to determne the dfference n head, tme, and group of head. Woodall and Ncube [5] nvetgated the multvarate CUSUM control procedure and defned the out-of-control condton for a ytem comprng everal chart. Ther procedure for ndependent qualty charactertc can be appled to the mult-tage and mult-tream manufacturng ytem. Nelon [6] propoed and developed group control chart for a ngle tage proce wth multple tream. He ponted out that f the output tream are hghly correlated then a ngle chart can be ued to montor the output from the multple tream, but f the output tream are not correlated then eparate chart for each tream hould be ued. Montgomery [3] revewed Nelon [6] approach for mult-tream proce. He dcued the control cheme for detectng a hft n the mean of all of the product tream and alo for detectng a hft n the mean of an ndvdual product tream n the multple tream proce. To detect a hft n the mean of all of the tream he uggeted takng a ample from each of the tream and then plottng the larget and mallet ample mean. He alo preented table of out-of-control average run length (ARL) for varou number of tream and conecutve tme that a partcular tream ha the larget (or mallet) value. Mortell and Runger [7] propoed a par of control chart for montorng a large number of tream. The frt chart (Shewhart chart) ued to montor hft common to all product tream and the econd chart (CUSUM chart) ued to montor a change n one tream wth repect to the other. Runger et al. [8] and Runger and Fowler [9] condered the hghly automated envronment wth dozen to hundred of tream. They howed how ome addtonal control chart could be ued to upplement the par of 766

2 chart recommended by Mortell and Runger [7]. Runger et al. [8] ued prncpal component analy to develop the control chart that are able to detect the agnable caue that affect all tream and agnable caue that affect one or a few tream n multple proce tream. Amn et al. [0] propoed the MaxMn EWMA control chart baed on the mallet (Mn) and larget (Max) obervaton n each ample. When there any change n the proce, the chart how whch parameter have ncreaed or decreaed. They explaned the degn procedure and mplemented the chartng technque n a ngle tage mult-tream proce. Zhang [], Fong and Lawle [2], Lawle et al. [3], Dng et al. [4] and Zantek et al. [5] dcued the varaton tranmon through multple proce tage. Nonethele, n all of the prevou tude, the chartng parameter (e.g. control lmt, ample ze or amplng nterval) have not been degned n an ntegratve and optmal manner. Intead, dentcal parameter value have been ued by each of the ndvdual chart. Tradtonally, each ndvdual chart n a chart ytem montorng a proce of a multtage manufacturng ytem degned n olaton. For example, n a tradtonal X chart ytem, ample ze n uually et around 5, the amplng nterval h manly decded by the workng hft (.e. the ratonal ubgroupng) and control lmt coeffcent k made dentcal (typcally taken a 3) for each chart n the ytem. In contrat, n an ntegrated chart ytem, all of the chart montorng the multtage manufacturng procee are degned n an ntegratve and optmal manner. The optmzaton degn of the ntegrated control chart ytem reult n dfferent n, h and k value or allocate dfferent power to dfferent chart n a ytem baed on the value of certan parameter (e.g. proce capablty, magntude of the proce hft) that would affect the performance of the control chart ytem. A a reult, the overall effectvene of the chart ytem mproved gnfcantly. Th artcle dcue the degn procedure and revew the avalable lterature on the optmzaton degn of the ntegrated control chart ytem. In Secton 2, the performance meaure and the optmzaton algorthm are brefly dcued. Secton 3 revew the avalable tattcal and economcal model for the optmzaton degn of the ntegrated control chart ytem. Fnally, Secton 4 draw concluon and gve ome drecton for the future reearch. 2. Degn of Integrated Control Chart Sytem The optmzaton degn of the ntegrated control chart ytem nvolve two maor tak, uch a to derve formula for the evaluaton of the performance of the chart ytem, and to develop algorthm for the optmzaton of the chartng parameter.e. ample ze n, amplng nterval h, and Lower Control Lmt LCL and Upper Control Lmt UCL of each chart n the chart ytem ( =, 2,, ; where, the number of tage n the chart ytem). 2. Performance Meaure In the tattcal degn, the performance of the control chart meaured by the frequency of the fale alarm and by the peed wth whch t detect the occurrence of agnable caue. Thu, the mot wdely ued tattcal meaure of performance are the n-control average tme to gnal ATS 0 and the out-of-control average tme to gnal ATS. On the other hand, n economcal degn, the control chart performance meaured n term of ome monetary value. The performance meaure ued n both tattcal and economcal degn of the ntegrated control chart ytem are brefly dcued bellow. 2.. Stattcal Degn Calculaton of n-control ATS 0 of the control chart ytem In a ngle tme unt, the probablty that the th control chart (or a duplcate of the th chart n a tream) n the th tage produce a fale alarm due to type I error probablty α approxmately equal to α /h. The probablty that t doe not produce a fale alarm nearly equal to ( - α /h ). Snce each of the g tream n the th tage run a duplcate of the th control chart, therefore, the probablty p 0 that the whole control chart ytem generate a fale alarm n a tme unt [, 6]. g = ( g p0 α / h ) = ( α / h ) () = 767

3 Fnally, ATS = p (2) 0 / 0 Calculaton of out-of-control ATS of the control chart ytem The out-of-control ATS of the ntegrated chart ytem defned a the average tme that one of the control chart n the chart ytem gve an out-of-control gnal ubequent to any proce n a manufacturng ytem gong out of control []. When one of the g parallel tream n the th tage ( ) out of control, the out-of-control ATS of the chart ytem calculated by, at = h (3) Z Z = ( w k tage out of control) (4) k= In Equaton (3), /Z the Average Run Length (ARL) of the chart ytem. The power Z of the chart ytem the probablty that an out-of-control cae happen n tage and gnaled durng a tme perod of h, and w k (k, k =, 2,, ) the probablty that tage k doe not gnal the proce hft durng a ame tme perod. The pecal feature of a multtage manufacturng ytem the dependency between the proce tage. If an out-ofcontrol cae occur n a tage the dependent downtream tage are affected. Therefore, a mechanm mut be developed to dentfy the effect between the proce tage and to determne the nduced proce hft due to the proce hft of the nfluencng tage. The power Z handle both the proce hft produced by the out-of-control tage telf and the nduced proce hft receved by the dependent downtream tage [, 2]. In ome applcaton, the proce tage may not be nterdependent; n thoe cae, the power Z doe not conder the nduced proce hft [6, 7]. Snce an out-of-control cae may occur n any of the tage, the fnal ATS for the control chart ytem h = = p ATS ( at p ) (5) Z where, p the probablty that the out-of-control cae take place n the th tage Economcal Degn Varou model have been propoed for economcally choong the control chart parameter. The advantage of the economcal degn model over the tattcal model are that they elect the chart parameter n uch a way that the total cot (ncludng the cot of npecton, cot of producng non-conformng tem, cot of detectng out-of-control gnal and other cot) mnmzed. That mean the economc model mnmze the expected total cot per unt tme aocated wth the SPC cheme. Many reearcher crtczed that the conventonal economc model generally have poor tattcal properte and produce exceve number of fale alarm. Moreover, the complex mathematcal model and optmzaton technque and, epecally, the dffculty n etmatng cot and other model parameter reult n the lack of practcal mplementaton of the economc chart. In vew of th, a mple model for the economcal degn of the ntegrated control chart ytem ha been propoed [8]. The total cot per unt tme aocated wth an ntegrated control chart ytem calculated baed on the deployed manpower n SPC actvte. C total = Cqualty + Cman (6) Both the qualty cot, C qualty and manpower cot, C man are drect or mplct functon of manpower M. C = C M (7) man m = C qualty q( δ ) L( δ ) f ( δ ) dδ (8) 0 MTBO Where, C m the manpower cot per operator per unt tme and MTBO the Mean Tme Between Out-of-control cae. The C qualty the cot ncurred by the out-of-control cae. It depend on the frequency (/MTBO) of the out- 768

4 of-control cae, the average number q(δ) of unt produced after the occurrence of a mean hft of ze δ, the expected lo functon L(δ) per product for a gven δ and, fnally, the dtrbuton of the mean hft δ. 2.2 Optmzaton Search Algorthm The earch algorthm for the optmzaton degn of the ntegrated control chart ytem qute dffcult a t nvolve many varable uch a n, h, LCL, UCL ( =, 2,, ). Some of the varable are nteger and other are fracton. The general trategy to earch from pont to pont untl the mprovement neglgble. Lke mot of the optmzaton tratege employed n SPC, the propoed algorthm make no attempt to ecure a global optmal oluton. Intead, t focue on dervng a convenent and ytematc procedure for dentfyng a atfactory and workable oluton that could be adopted n practce. Optmzaton of control lmt LCL and UCL of the chart ytem In the optmzaton degn, the control lmt LCL and UCL ( =, 2,, ) or equvalently the control lmt coeffcent (k, k 2,, k ) are replaced by the correpondng type I error probablte (α, α 2,, α ). The underlyng dea of the optmzaton degn to enhance the power of thoe chart whch take a very long perod to produce a gnal when the correpondng procee become out of control. Th procedure mut acrfce the power of ome other chart n the ytem. However, f the α value of all chart are aduted n an ntegratve and optmal manner, the overall (average) effectvene of the control chart ytem wll be mproved. Wu et al. [] propoe a dynamc earch algorthm where the followng equaton (Equaton (9)) ued to determne the range of poble α value n the th level earch. / g / τ α = h ( ) g (9) α / h =, where, τ the mnmum allowable n-control ATS 0. In the propoed algorthm, the optmal value of α of the frt ( ) control chart are earched tep by tep n ( ) level, ung the ame tep ze dα. The lat α fnally determned o that the reultant ATS 0 exactly equal to the pecfed value (.e. the fale alarm rate not ncreaed). Optmzaton of ample ze n and amplng nterval h of the chart ytem The optmzaton of n and h ( =, 2,, ) enure that no extra manpower (or the tme pend on SPC actvte) requred. A gradent baed earch algorthm [2] employed to approach the optmal et of n and h tep by tep. The amount of manpower M requred by an ntergrated chart ytem n gt M = (0) h The mnmum ncrement of ample ze n one. Therefore, the tep ze ( n ) of n for all tage taken a one. Then, for an ncrement ( n = ) of every ample ze, the correpondng manpower ncrement M gt M n = n = () n h It ratonal to make the tep ze h of h proportonal to h telf, that h h, or, h = bh (2) where, b (b > 0) a proportonalty contant. Then, for a decrement of (- h ) of every amplng nterval, the ncrement of manpower M n = gt = n gt M h ( h ) ( bh ) = b (3) 2 h h h By equatng M n and M h, g = t n gt b (4) h h Generally, th b value wll make the ncrement of M due to a decreae of h by one h mlar to the ncrement of M becaue of an ncreae of n by one n. 769

5 Now, the ample ze n and the amplng nterval h can be ncreaed or decreaed tep by tep wth the tep ze n and h. It well known that, ncreang n by n reult n decreae of out-of-control ATS (or ganng detecton power) and decreang n by n reult n ncreae of ATS (or long detecton power). Converely, decreang h by h mean movng the amplng nterval n the ganng drecton and ncreang h by h mean movng the amplng nterval n the long drecton. If all n and h are ubttuted by the general varable X ( =, 2,, 2) (.e. an X may be a ample ze or a amplng nterval), the ganng factor G pertanng to an X for an ncrement of manpower M gven by (uppoe the obectve to mnmze the out-of-control ATS of the chart ytem), ATS ATS G = = (5) M M X X where, ATS the change n the out-of-control ATS when an X move one tep n the ganng drecton (.e. for n, or - h for h ) and all other X are kept unchanged. The quantty ATS alway maller than zero. Specfcally, f an X a ample ze, ATS ATS ( ATS ) h G = = = (6) M g t g t n () n h And f an X a amplng nterval, ATS ATS ( ATS ) h G = = = (7) M n g t n g t b h ( )( bh ) 2 h h If the ganng factor G of an X larger, then, when th X move n the ganng drecton, greater reducton n ATS wll be obtaned wth relatvely maller ncreae n M. Converely, a lower G mean that f the correpondng X move n the long drecton, greater reducton n M wll be obtaned wth relatvely maller ncreae n ATS. Therefore, the general varable X are frt ranked accordng to the decendng order of G. Then, at each degn pont, N general varable X wth the larget G value wll be moved one tep n ther ganng drecton (that, f an X a ample ze, ncreae t by n ; f an X a amplng nterval, decreae t by h ). Th wll uually lead to a ubtantal reducton n ATS wth an ngnfcant ncreae of M. In order to balance out the ncreae n M, the ret (2 - N) general varable X wth maller G wll be moved one tep n ther long drecton. Th econd movement may adverely ncreae ATS, but th ncreae n ATS mut be maller than the decreae of ATS n the frt movement. A earchng mechanm employed to dentfy the maxmum poble value for N, whch enure that, n each earch tep, the maxmum reducton n ATS acheved, and meanwhle, the requred manpower M equal to the pecfed value. 3. Avalable Model for the Optmzaton Degn of the Integrated Control Chart Sytem Few model have been developed baed on the performance meaure and the optmzaton algorthm decrbed n Secton Stattcal model Integrated X control chart ytem Wu et al. [], Lam et al. [2], and Shamuzzaman et al. [6] developed ntegrated X control chart ytem for montorng proce mean at dfferent proce tage n a multtage manufacturng ytem. The optmzaton degn mnmze the out-of-control ATS of the chart ytem on condton that nether the fale-alarm rate nor the requred manpower greater than the pecfed value (the calculaton of ATS 0 and ATS are brefly dcued n ecton 2..). In ome applcaton, the change of ample ze (n ) and amplng nterval (h ) at dfferent proce tage may not be allowed becaue of fxed workng hft or fxed reource allocaton or other dffculte. Under uch crcumtance, the lower control lmt (LCL ) and upper control lmt (UCL ) can be ealy aduted wthout changng the regular workng chedule. The optmzaton of LCL and UCL ( =, 2,, ) mprove the performance of the 770

6 chart ytem to ome degree [, 6]. However, the optmzaton of n and h ( =, 2,, ) n addton to the optmzaton of LCL and UCL further enhance the effectvene of the chart ytem [2]. Some ueful gudelne are alo provded to ad the uer to adut the ample ze, amplng nterval and control lmt of the control chart n a ytem, even when more complcated computaton ha not been carred out. Accordng to the gudelne [2], the followng chart hould be made more powerful, () The control chart that ued n a tage wth maller number of tream; and/or (2) The control chart that ued to montor a proce wth larger varance; and/or (3) The control chart that ued to montor a proce wth maller allowable mean hft; and/or (4) The control chart that ued to montor a proce tage where an out-of-control cae more lkely to occur; and/or (5) The control chart that ued to montor a proce tage where the tme requred to npect a unt maller; and/or (6) The control chart that ued to montor a tage the qualty charactertc of whch depend on that of other tage. Integrated X &S control chart ytem Wu and Shamuzzaman [7], and Shamuzzaman and Wu [9] developed the ntegrated X &S control chart ytem for montorng the mean and varance of the procee n dfferent tage n a manufacturng ytem. It degn control lmt, a well a ample ze and amplng nterval, of all the X chart and S chart n a ytem n an ntegratve and optmal manner. The degn algorthm optmally allocate the detecton power of the ytem among dfferent tage a well a between the X chart and S chart wthn each tage baed on the value of certan parameter uch a proce capablty and magntude of the proce hft that would affect the performance of the chart ytem. A parameter T called the average nformatve tme ued to meaure the performance of the X &S chart ytem. h p T = (8) z where, z the power of the out-of-control tage, that, the power generated by the X &S chart n a tream n tage when proce hft occur n th tream. Lke the out-of-control ATS, the maller T, the more effectve the chart ytem n detectng out-of-control cae. The conderaton of the power due to the nduced proce hft receved by the dependent downtream tage not only ncreae the complexty of the degn procedure, but may alo mlead the follow-up nvetgaton of the agnable caue and ncreae the Mean Tme To Repar (MTTR) [7]. In vew of th, the optmzaton model propoed n degnng the ntegrated X &S chart ytem mnmze the average nformatve tme T (conderng only the power due to the proce hft of the out-of-control tream) rather than the out-of-control ATS (conderng both the power due to the proce hft of the out-of-control tream and the power due to the nduced proce hft are becaue of the dependency between the proce tage). Integrated TBE control chart ytem In today manufacturng ndutry, procee have acheved a low level of nonconformte or defect due to technologcal advancement and automaton. In a low defect envronment, qualty control baed on tradtonally ued Shewhart chart reult n hgh fale alarm rate and nablty to detect further proce mprovement. The ue of tme between event (TBE) chart may be a good alternatve n a low defect envronment. The TBE chart montor the tme between ucceve event, where, the tme between two ucceve event exponentally dtrbuted. The man advantage of TBE chart are that t doe not need any ubectve ample ze, and t can detect further proce mprovement. Shamuzzaman et al. [20] developed a control chart ytem contng of everal ndvdual TBE chart, each of whch ued to montor the tme between ucceve event at dfferent proce tage n a multtage manufacturng ytem. The term event defned a the producton of defect and the term tme refer to the tme between the occurrence of the event. The propoed model degn the control lmt of all the TBE chart n a ytem n an ntegratve and optmal manner n order to mnmze the out-of-control ATS of the ytem. The fale alarm rate ued a the contrant. 77

7 3.2 Economcal Model Integrated X control chart ytem Wu et al. [8] develop a model for the economc degn of the ntegrated X chart ytem for montorng multtage manufacturng procee. The degn algorthm mnmze the total cot ncludng manpower cot and qualty cot (a decrbed n Secton 2..2) aocated wth the mplementaton of the SPC ytem baed on the amount of allocated manpower and the random proce hft. The man focu on the optmal deployment of the manpower M to the SPC ytem. In the mean tme, the ample ze, amplng nterval and control lmt are alo optmzed. The whole optmzaton proce carred out n three level. The hgh-level optmzaton a nglevarable earch for the optmal value of M ung the Succeve Quadratc Etmaton method. Then, for a value of M determned n the hgh level, md-level earch [2] employed to fnd the optmal value of n and h ( =,2,, ). Fnally, a dynamc low-level earch [] nvoked to fnd the optmal LCL and UCL ( =,2,, ) whch ontly make the reultant ATS 0 exactly equal to the pecfed value and, n the mean tme, mnmze the total cot for a et of value of (M, n, h ) that are determned n the hgh and mddle level (the md- and low-level earche have been brefly decred n Secton 2.2). Some ueful gudelne are alo provded o that the uer can deploy manpower to dfferent SPC ytem ratonally and effectvely. Accordng to the gudelne [8], a relatvely large amount of manpower hould be deployed f, () The producton rate hgh; and/or (2) The cot for fxng an out-of-pecfcaton product hgh; and/or (3) The npecton rate of an npector hgh; and/or (4) The requred n-control ATS 0 hgh; and/or (5) The upper pecfcaton lmt mall; and/or (6) The mean tme between out-of-control cae mall; and/or (7) The manpower cot low; and/or (8) The mean value of the proce hft low. Integrated TBE control chart ytem The mplementaton of the TBE chart ytem ha gnfcant economc mpact a t nvolve varou cot, uch a the cot ncurred by the occurrence of the event, cot of fale alarm, cot of locatng and removng the agnable caue and cot of allowng the ytem to operate n an out-of-control tate. Zhang et al. [2] ntroduced thee ue n the algorthm for the optmzaton degn of the economc ntegrated TBE chart ytem. It degn control lmt of all the TBE chart n a ytem n an ntegratve and optmal manner n order to maxmze the proft aocated wth the mplementaton of the SPC ytem. The fale alarm rate ued a the contrant. 4. Concluon and Future Reearch Th artcle decrbe degn technque and revew the avalable model on the optmzaton degn of the ntegrated control chart ytem for montorng multtage manufacturng procee. It found that the ntegrated degn algorthm mprove the ytem performance gnfcantly. The optmzaton degn alo enure that no extra reource for conductng the qualty control actvte are requred and the fale-alarm rate not ncreaed. The degn of the ntegrated chart ytem more dffcult than that of the tradtonal chart ytem. However, the degn procedure can be ealy computerzed. The degn of an ntegrated chart ytem to be conducted only once, and the reultant ytem can be ued contnuouly untl the proce parameter are changed. The performance meaure and the optmzaton degn algorthm of the ntegrated X, X &S, and TBE chart ytem are avalable n the lterature (a ummary of the avalable lterature are hown n Table. Intereted reader are alo referred to [22]). However, there are tll many reearch topc n the ame drecton and can be conducted n the future. () The Shewhart X chart a well a the X &S chart are condered a the mot wdely ued varable control chart becaue of ther mplcty for mplementaton and eay to undertand. However, the Shewhart chart relatvely nentve to mall hft n the proce. Two mportant alternatve to the Shewhart control chart may be ued when the hft n the proce are mall. They are the CUSUM control chart and the EWMA 772

8 control chart. Future reearch can develop the ntegrated control chart ytem conderng the CUSUM chart and the EWMA chart (2) Attrbute chart are generally not a nformatve a varable chart becaue there typcally more nformaton n a numercal meaurement than n a mere clafcaton of the conformty or the nonconformty. However, the attrbute chart do have mportant applcaton. They can help move the frm procee toward a zero percentage defectve rate. They are partcularly ueful and neceary n ervce ndutre, healthcare, and other non-manufacturng ecton, nce many qualty charactertc found n thee ecton are not ealy meaured on a numercal cale. Therefore, future reearch can develop the ntegrated control chart ytem conderng the attrbute control chart uch a the p chart and the np chart. The ntegrated degn of the p chart or the np chart wll further mprove the performance of the chart ytem. (3) Some reearcher propoed the algorthm for the degn of the adaptve (or dynamc) control chart cheme, n whch ether the ample ze or amplng nterval or both are changed dependng on the value of the amplng tattc. Further reearch can develop the adaptve ntegrated control chart ytem for a manufacturng ytem. (4) The concept of the ntegrated TBE control chart ytem can be ued to develop a control chart ytem for machne or machne component relablty montorng n a multtage manufacturng ytem (5) The degn of ntegrated control chart ytem for montorng dfferent procee of a ob-hop manufacturng ytem or hort producton run may be an nteretng work. (6) The avalable lterature on the optmzaton degn of the ntegrated control chart ytem conder unvarate qualty charactertc. In many applcaton, the qualty of a product depend on more than one charactertc. Producng product wth multple qualty charactertc alway one of the concern for an advanced manufacturng ytem [23]. The concept of the unvarate ntegrated control chart ytem can be appled to develop a control chart ytem for montorng multvarate qualty charactertc n a multtage manufacturng ytem. (7) The avalable model on the ntegrated control chart ytem ue a eparate chart for montorng the output of each ndvdual tream (e.g. machne) n a tage; uually, the parallel tream n a tage of a multtage manufacturng ytem have the ame mean, tandard devaton and target [8], and therefore, all of them ue an dentcal control chart. Th mean that the number of chart n the chart ytem ncreae a the number of machne n dfferent tream and tage of the manufacturng ytem ncreae. Practcally, t may be dffcult to handle all the chart n a chart ytem montorng a large manufacturng ytem. It wll alo ncreae the complexty n dagno of the out-of-control tream or tage. Future reearch can check the poblty of ung a ngle chart for montorng all the parallel tream n a tage; th wll reduce the number of chart n the chart ytem to a gnfcant degree and mplfy the montorng proce. Type of control chart ytem Integrated X chart ytem Table. Summary of the lterature on the ntegrated control chart ytem Stattcal degn Economc degn Parameter optmzed Parameter optmzed LCL, UCL n, h, LCL, UCL LCL, UCL M, n, h, LCL, UCL Wu et al. (2004) Lam et al. (2005) --- Wu et al. (2007) Shamuzzaman et al. (2005) Integrated X &S chart ytem Wu and Shamuzzaman (2005) Shamuzzaman and Wu (200) Integrated TBE chart ytem Shamuzzaman et al. (2009) --- Zhang et al. (20) --- Acknowledgement Th artcle preent a revew note on the optmzaton degn of the ntegrated control chart ytem and provde ome reearch drecton for ntereted reader. The author gratefully acknowledge the contructve comment and uggeton of the revewer. 773

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